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Stochastic control, entropic interpolation and gradient flows on Wasserstein product spaces
[article]

2016
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arXiv
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pre-print

Since the early nineties, it has been observed that the Schroedinger bridge problem can be formulated as a stochastic control problem with atypical boundary constraints. This in turn has a fluid dynamic counterpart where the flow of probability densities represents an entropic interpolation between the given initial and final marginals. In the zero noise limit, such entropic interpolation converges in a suitable sense to the displacement interpolation of optimal mass transport (OMT). We

arXiv:1601.04891v1
fatcat:jw3yx4tgtjaajcxve5cw7ebwyi